A Classification Theorem for Admissible Standard-Model Structures

This paper proves a classification theorem for admissible Standard-Model-level bookkeeping structures, assuming the previously established kernel constraints of admissibility, standing, identity-preserving redescription, and transport completeness. The target is not a new dynamical model, a derivation of numerical parameter values, or a prohibition on broader UV or BSM theories. The target is narrower: to classify the admissible bookkeeping structures capable of supporting stable, reusable Standard-Model observables. The main result is that, once the accepted kernel constraints are applied jointly, the admissible same-regime solution space contains a single occupant up to admissible equivalence. Apparent alternatives either collapse under the standing quotient, fail transport completeness, introduce non-admissible parameter freedom, change load or scope, or reduce to skin-level redescription. The Standard Model bookkeeping structure is therefore not selected by empirical adequacy, convention, or representational preference; it is the unique minimal standing-preserving occupant of the admissible bookkeeping space. The paper also distinguishes this result from fixed-load closure theorems: prior work establishes the admissibility kernel and same-load interior closure, whereas the present paper proves the global classification of admissible occupants in the Standard-Model regime. Remaining numerical inputs are certified as boundary data rather than as competing structures.